US11169120B2 - Method for the ultrasound detection and characterization of defects in a heterogeneous material - Google Patents

Method for the ultrasound detection and characterization of defects in a heterogeneous material Download PDF

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US11169120B2
US11169120B2 US17/272,844 US201917272844A US11169120B2 US 11169120 B2 US11169120 B2 US 11169120B2 US 201917272844 A US201917272844 A US 201917272844A US 11169120 B2 US11169120 B2 US 11169120B2
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point
amplitude
different
probe
probed
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US20210310991A1 (en
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Paul KASSIS
Nicolas Paul
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Electricite de France SA
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/04—Analysing solids
    • G01N29/06—Visualisation of the interior, e.g. acoustic microscopy
    • G01N29/0654—Imaging
    • G01N29/069—Defect imaging, localisation and sizing using, e.g. time of flight diffraction [TOFD], synthetic aperture focusing technique [SAFT], Amplituden-Laufzeit-Ortskurven [ALOK] technique
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/04—Analysing solids
    • G01N29/043—Analysing solids in the interior, e.g. by shear waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/22—Details, e.g. general constructional or apparatus details
    • G01N29/26—Arrangements for orientation or scanning by relative movement of the head and the sensor
    • G01N29/262—Arrangements for orientation or scanning by relative movement of the head and the sensor by electronic orientation or focusing, e.g. with phased arrays
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/10—Number of transducers
    • G01N2291/106—Number of transducers one or more transducer arrays

Definitions

  • the present invention relates to the non-destructive testing of materials, and more precisely to the detection and characterisation by ultrasound of defects in a heterogeneous material.
  • Ultrasound is commonly used for implementing non-destructive testing of materials.
  • an ultrasonic transducer positioned at the surface of the material to be examined is used, that emits ultrasonic waves in the material. These waves propagate in the material and are reflected by the latter according to its structure. The transducer receives these reflected waves, and the analysis thereof permitting to detect any defects in the material.
  • the phenomenon of diffusion of the ultrasonic wave by the structure of the material becomes preponderant. This diffusion can then lead to the generating of a structure noise, i.e. to an ultrasonic signal with a non-negligible amplitude received by the transducer and having characteristics that are similar to those that a wave reflected by a defect would emit, thus resulting in a deterioration of the capacity for detecting defects that are actually present in the material.
  • a structure noise i.e. to an ultrasonic signal with a non-negligible amplitude received by the transducer and having characteristics that are similar to those that a wave reflected by a defect would emit, thus resulting in a deterioration of the capacity for detecting defects that are actually present in the material.
  • the structure noise has time and spectral characteristics that are similar to those of the defect signatures that form the useful signal, the conventional approaches for processing ultrasonic signals, by time or frequency filtering, deconvolution or projection on wavelet bases are ineffective.
  • Patent application US 2007/0006651 A1 describes a method of non-destructive testing using ultrasonic waves, based on comparing the amplitude of the frequency spectrum of a selection of the signal with a reference amplitude. This application mentions the possibility of taking measurements at different positions and mentions combining these measurements in order to obtain an average measurement signal in the spatial direction. However, such a method does not provide complete satisfaction, and the signal remains tainted with noise.
  • Patent application WO2016083759 describes a method for the ultrasound detection and characterisation of defects in a heterogeneous material, comprising the following steps:
  • f ⁇ ( t ) ( ⁇ ⁇ ⁇ z ⁇ ⁇ x ⁇ ( z , t ) - m ⁇ ( t ) ⁇ ⁇ ) ⁇ with ⁇ , ⁇ and ⁇ different from zero, x(z,t) the time-dependent signal representative of the amplitude of the sound propagated in the material as a function of time for a position z of the ultrasonic receiving transducer, and m(t) a function of time,
  • Patent application WO2016083759 thus describes a pre-processing that makes use of a time-dependent function representative of a spatially-averaged power of the time-dependent signals corresponding to different positions of the ultrasonic receiving transducer.
  • Such a pre-processing makes permits improving the detection and characterisation of defects in the material by homogenising the signals processed, so that the noise statistics are similar at the different measurement locations, facilitating the detection of an abnormal signal level.
  • the measurement noise still exists and can sometimes limit the capacities of detecting and characterising a defect.
  • the method does not make use of all the capacities of a multi-element probe comprising a plurality of transducers, operating as an emitter or as a receiver. Indeed, the acquisition of measurement signals using such a multi-element probe gives rise to additional characteristics in the measurement signal that can be used to further improve the detecting and the characterising of defects in the material.
  • the present invention has for purpose to propose a method for ultrasound detection of defects in a heterogeneous material that allows reducing the influence of the structure noise that taints the data collected.
  • N s a number of images of different probe positions taken into account, Ns being greater than 2
  • V w a set of points around the point w that can be reduced to the point w
  • I(z i , w j ) being the amplitude or the absolute value of the focused amplitude at the probe position z i for the point w j , with more preferably,
  • N s a number of images of different probe positions taken into account, Ns being greater than 2, V w a set of points around the point w that can be reduced to the point w, I(z i , w j ) being the amplitude at the probe position z i for the probed point w j , and N v the cardinal of the set of points V w ;
  • N s ′ a number of images of different probe positions
  • V w ′ a set of points around the point w that can be reduced to the point w
  • A(w) the measure of central tendency
  • V w a set of points around the probed point w that can be reduced to the probed point w
  • I(z i , w j ) being the focused amplitude at the probe position z, for the probed point w j
  • N v the cardinal of V w
  • A(w) a measure of central tendency of the focused amplitude at the probed point on different probe positions
  • the invention also relates to a computer program product comprising program code instructions for the execution of the method according to the invention when said program is executed on a computer.
  • the computer program product takes the form of a non-transitory tangible medium that can be read by a computer, on which program code instructions are stored for the execution of the method according to the invention when the medium is read by a computer.
  • FIG. 1 shows the inspection of a tube by a multi-element probe
  • FIG. 2 is a diagram that diagrammatically shows steps of the method according to a possible embodiment of the invention.
  • FIG. 3 a is an example of an image resulting from the implementation of a total focusing method on a heterogeneous material, before the implementation of the correction proposed by the invention
  • FIG. 3 b is an example of an image corrected by the implementation of the correction proposed on the image of FIG. 3 a
  • FIG. 3 c is an example of a filtered image resulting from a spatial filtering using a bilateral filter on the corrected image of FIG. 3 b.
  • Such an acquisition of measurements of transducers is commonly carried out, in particular for the implementation of the so-called TOFD technique (time of flight diffraction), of which the same acquisition protocol can be implemented for the present invention.
  • TOFD technique time of flight diffraction
  • a common material for the tubes is for example inconel, i.e. an alloy with mainly a nickel, chrome, and iron base, and also containing copper, manganese and molybdenum, as well as optionally other components in generally lesser quantities.
  • This is a heterogeneous material of which the structure has grains of a size comparable to the wavelength of the ultrasonic waves used in non-destructive testing.
  • the frequency of the ultrasonic waves generally used in non-destructive testing can range from 0.1 to 50 MHz, with the band 2-10 MHz being the most commonly used.
  • the wavelength, in this band is therefore comprised practically, for metals such as steel or aluminium, between 3 mm and 0.5 mm. Note that the method is not necessarily restricted to a heterogeneous material, but here is of an advantageous application.
  • a first step (step S 1 ) of the method consists of acquiring a set of measurement data grouping together a measurement signal representative of the amplitude of the ultrasound propagated in the material as a function of time for several probe configurations at several positions of a multi-element probe 1 .
  • the acquisition is done by means of a multi-element probe 1 comprising a plurality of transducers 14 , 15 .
  • the probe 1 is disposed facing the inner wall 11 of this tube 10 , at a position z.
  • the tube 10 has a defect 13 , represented here in the form of a gash.
  • the transducers 14 , 15 are more numerous and have a spatial distribution that varies according to the intended applications and the surfaces to be inspected.
  • the spatial distribution can for example be as a matrix, annular or forming a strip, for the most common, or have particular patterns.
  • the plurality of transducers 14 , 15 gives the possibility of focusing the emitted waves in the desired direction and at the desired depth. It is thus possible to inspect a plurality of probed points w.
  • the spatial distribution of the transducers 14 , 15 may not be plane, so as to conform to the surface to be inspected. It is common to use a coupling medium such as a sole or a layer of coupling gel, so as to favour the propagation of the ultrasound between the transducers 14 , 15 and the material.
  • the multi-element probe 1 scans the surface of the material to be inspected, and therefore scans a plurality of positions z at the surface of the material.
  • the multi-element probe 1 can scan the inner surface 11 of the tube 10 helically.
  • the position z of the multi-element probe 1 at the surface 11 of the tube 10 can for example be expressed by a depth p and an angle ⁇ , the positions z being spaced apart for example by less than one millimetre in altitude and by a few degrees (typically less than two degrees) in angle.
  • Other ways of expressing the position z can be used according to the conformation of the surface to be inspected. In the case of a plane surface, the position could thus be expressed with an abscissa instead of the angle.
  • one or several emitting transducers 14 emit (step S 11 ) ultrasonic waves that penetrate into the tube 10 at its inner wall 11 , then propagate in the material of said tube 10 , before being received by another transducer 15 , referred to as receiving transducer (step S 12 ).
  • step S 11 ultrasonic waves that penetrate into the tube 10 at its inner wall 11 , then propagate in the material of said tube 10 , before being received by another transducer 15 , referred to as receiving transducer (step S 12 ).
  • first travel 16 forming a short path for the ultrasonic waves, which are diffracted by the defect 13 in the direction of the receiving transducers 15
  • second travel 17 forms a long path for the ultrasonic waves, which are reflected by the outer wall 12 of the tube 10 in the direction of the defect 13 then join the receiving transducer 15 .
  • measurement signals are acquired according to different configurations of the multi-element probe 1 .
  • These different configurations can vary between them for example by the roles played by each one of the transducers 14 , 15 .
  • the transducers 14 , 15 can preferably alternatively play the role of emitter or the role of receiver.
  • a transducer 14 , 15 can be an emitter, and become a receiver during another iteration.
  • a set of measurement data grouping together the measurement signal is obtained for each configuration for each probe position z. More precisely, for each probe position z, an acquisition matrix of coefficients x(z, n, i, j) is obtained each corresponding to the amplitude of the measurement signal x at instant nTe (Te being the sampling period) received by the transducer j when the transducer i emits ultrasonic waves.
  • a focusing method on the set of data is then implemented, in order to obtain (step S 2 ) an image wherein each pixel of the image represents a probed point w of the material with which a focused amplitude is associated for said probed point w on different probe positions z, and which is not a function of time or of the configuration of the multi-element probe 1 (i.e. independently of which transducer 14 , 15 is acting as emitter i or receiver j).
  • the probed point w is a position in the material, which can be expressed for example as a vector with two or three spatial coordinates, typically expressed in a coordinate system related to the position z of the multi-element probe 1 .
  • a common focusing method is the total focusing method commonly designated by the acronym TFM.
  • TFM total focusing method
  • the different configurations can be distinguished from one another by emitter or receiver functions fulfilled by different transducers 14 , 15 .
  • a first transducer 14 or a first set of transducers 14
  • an electrical pulse signal so as to emit ultrasounds.
  • These ultrasounds propagate in the material, and are then acquired by all the transducers 14 , 15 (or by a second set of transducers 15 ).
  • another transducer 14 or another first set of transducers 14
  • each one of the transducers 14 , 15 emits ultrasounds in at least one probe configuration at a position z.
  • each one of the transducers 14 , 15 is in turn the sole emitting transducer, while all the transducers 14 , 15 acquire the ultrasounds. There are then as many configurations as there are transducers 14 , 15 .
  • M is the number of transducers 14 , 15 of the multi-element probe 1
  • h(w, i, j) is a function representative of the travel of the ultrasonic waves between the transducer i that emits these waves and the transducer j that receives them, passing through the probed point w.
  • h(w, i, j) corresponds for example to the travel time (expressed as a number of samples) estimated for one ultrasonic wave:
  • this can be the estimated travel time of an ultrasonic wave using the short path 16 in FIG. 1 between the transducer 14 that emits and the transducer 15 that receives.
  • h(w, i, j) can also correspond to an estimated travel time for one ultrasonic wave:
  • this can be the estimated travel time of one ultrasonic wave using the long path 17 in FIG. 1 between the transducer 14 that emits and the transducer 15 that receives, which is reflected by the outer wall 12 of the tube 10 .
  • This type of travel is rather used for the defects that open onto the outer wall 12 of the tube 10 .
  • These travel times can be estimated using speeds of the ultrasonic waves which depend on the frequency of the ultrasonic waves and on the nature of the material inspected, and also the type of propagation (transverse waves or longitudinal waves). Conversions of the propagation mode can also be considered during different reflections.
  • the function g is a function that can for example depend on the position of the probed point w or on the propagation speed of the wave.
  • the function g can also be the absolute value function, or the analytical signal module.
  • Those skilled in the art can for example refer to documents that have different total focusing methods.
  • the doctoral thesis in physics of Uduardo R. lopez Villaverde of April 2017 entitled “ Imagerie Ultrasonore dans des develop complexes par focalisation en tous points: Développement d'unepole de débruitage des images basées sur la décomposition de l'hearted de writefulness temporel ” describes a recent state of the art of certain total focusing methods.
  • each pixel of the image represents a probed point w of the material with which a focused amplitude I(z,w) is associated.
  • the PWI method is based on the emission of plane waves by exciting all the transducers 14 , 15 unisequentially, which makes it possible to orient and increase the amplitude of the incident field in the desired directions.
  • An incident plane wave is formed by exciting all or a portion of the transducers 14 , 15 with a temporal offset between the transducers 14 , 15 . By changing the temporal offset between the emissions of the transducers, the angle of propagation Ok of the plane wave is modified.
  • the different configurations use different angles of propagation Ok, obtained by different temporal offsets, i.e. different delays applied to the emission of ultrasonic waves.
  • the transducers 14 , 15 then each acquire a measurement signal representative of the amplitude of the ultrasound propagated in the material.
  • the measurement signals received at each ultrasonic firing are focused at reception at all points inspected.
  • this plane wave Due to the fact that the transducers 14 , 15 emit ultrasound with temporal offsets in such a way as to emit a plane wave in the material, this plane wave has an angle of propagation that depends on the temporal offset between the transducers. By varying this temporal offset between transducers 14 , 15 , plane waves can be emitted with different angles of propagation.
  • M is the number of transducers 14 , 15 of the multi-element probe 1
  • ⁇ k is the angle of propagation (or angle of incidence) of the plane wave emitted, No being the number of angles of propagation, and therefore of different temporal offsets
  • h(w, ⁇ k , j) is a function representative of the travel of the plane wave of angle of propagation ⁇ k to the transducer j that receives it, passing through the probed point w.
  • h(w, ⁇ k , j) corresponds for example to the travel time (expressed as a number of samples) estimated for:
  • the travel times can be estimated from the speeds of the ultrasonic waves which depend on the frequency of the ultrasonic waves and on the nature of the material inspected, and also on the type of propagation (transverse waves or longitudinal waves).
  • the function g is a function that can for example depend on the position of the probed point w or on the propagation speed of the wave.
  • each probe position z an image in which each pixel of the image represents a probed point w of the material with which a focused amplitude is associated for said probed point w on different probe positions z.
  • the image can be in two dimensions (if w is of dimension 2) or in three dimensions (if w is of dimension 3).
  • the detecting then the characterising of a defect is then carried out from the values taken by this focused amplitude I(z,w), typically from the absolute value
  • I(z,w) For the purposes of clarity and simplification, reference hereinafter to the focused amplitude I(z,w) will indifferently designate said focused amplitude I(z,w) or its absolute value
  • the structure noise observed on the images coming from TFM has a spatial inhomogeneity: the extent of the structure noise varies according to the location of the probed points w. In particular, it tends to be higher in the vicinity of the transducers 14 , 15 . It is therefore proposed to proceed with a post-processing of the images obtained aiming to homogenise then to reduce the structure noise, so as to improve the detecting and the characterising of the defects.
  • the post-processing proposed is based on making use of statistics drawn from the multiplicity of the data available for the same probed point w, due to the fact that information on the same probed point w in the material appears in different images concerning different positions z.
  • step S 3 consists in determining, for each probed point w, a measure of central tendency, noted as A(w) of the focused amplitude I(z,w) at the probed point w on different positions z of the multi-element probe 1 .
  • the measure of central tendency A(w) is an average or a median.
  • the measure of central tendency is an average A(w) having general formula:
  • N s a number of images of different probe positions z taken into account, Ns being greater than 2
  • V w a set of points around the probed point w that can be reduced to the probed point w
  • I(z i , w j ) being the focused amplitude or the absolute value of the amplitude at the position z i for the probed point w j .
  • the set of points V w includes the probed point w, and is more preferably centred around the probed point w. Its size is chosen according to the characteristics of the structure noise and of the images used. For example, the set of points V w can be chosen as all the greater as the number of images N s of different probe positions z taken into account is small. Indeed, taking the vicinity of the probed point w into account makes it possible to calculate the measure of central tendency on enough points and thus to obtain a bester estimation of the measurement of central tendency. However, the set of points V w preferably groups together less than 100 points around the probed point w, so as to retain the local aspect of the measure of central tendency, which has to remain representative of the focused amplitude at the probed point w, i.e.
  • step S 4 consists of determining, for each probed point w, a function B(w) representative of the variability of the focused amplitude at this probed point w on the different positions z of the multi-element probe 1 .
  • the function B(w) typically has general formula:
  • N s ′ a number of images of different probe positions z
  • V w ′ a set of points around the probed point w that can be reduced to the probed point w
  • N v′ the cardinal of V w ′.
  • I(z,w) here designates the absolute value of the focused amplitude.
  • step S 5 it is possible to correct (step S 5 ) on each image the amplitudes associated with the probed point w considered. This correction is made by subtracting the measure of central tendency A(w) from the focused amplitude I(z,w) and by dividing by the function B(w) representative of the variability.
  • of the focused amplitude is used.
  • Corrected images are then obtained that can be used to detect and characterise the defects of the material (step S 6 ), with an improved highlighting of the defects, and a better characterisation of the latter thanks to the correction proposed.
  • FIGS. 3 a and 3 b show the implementation of the normalisation on an example of an image coming from a TFM for a position z of the multi-element probe 1 .
  • These images come from measurements on a model that has a defect 13 of 0.5 mm in diameter located at a depth of 5 mm.
  • the vertical axis represents the depth (in arbitrary units), and the horizontal axis the abscissa (in arbitrary units).
  • a dark shade indicates a low value, while a light shade indicates a high value.
  • the focused amplitude I(z,w) can be simply noted as I(w).
  • the corrected amplitude can be noted I c (w).
  • the position of a probed point w being located by an abscissa a and a depth p
  • the focused amplitude can be noted as I(a, p)
  • the corrected amplitude as I c (a, p)
  • FIG. 3 a is therefore an example of an image, before the implementation of the correction. It is observed that the image has a fast gradient from the top of the image, corresponding to the surface 11 , from high values (light shades) to lower values (dark shades), in such a way that the image can be divided into two parts: a top part 31 having light shades, and a bottom part 32 having only dark shades.
  • the presence of the defect 13 in the material is materialised by a light zone 35 in the top part 31 , which however is hardly distinguishable from the light shades of this top part 31 .
  • FIG. 3 b is an example of a corrected image corresponding to the image of FIG. 3 a after implementation of the proposed correction.
  • the top part 31 is no longer distinguishable from the top part 32 .
  • the gradient of shades has indeed disappeared from the top part 31 , while isolated light zones and of a low extent have appeared in the top part 31 as well as in the bottom part 32 , which therefore no longer has only dark shades.
  • the light zone 35 corresponding to the presence of the defect 13 is now clearly distinguished in the top part.
  • the proposed correction has therefore made it possible to highlight the presence of the defect in the top part 31 .
  • the modification of the amplitudes corrected in the bottom part 32 made it possible to ensure the absence of a defect in this bottom part 32 .
  • the presence of a possible defect in the bottom part 32 would not have appeared in the image of FIG. 3 a due to the fact that the focused amplitudes would have been so low that they would not have been distinguished from the structure noise.
  • the method of correction would have made it possible to highlight any defect, as shown by the isolated light zones and of low extent appearing in the bottom part 32 .
  • the detecting and the characterising of defects is preferably carried out from the image.
  • Defects such as gashes can extend over several tens of millimetres.
  • the points of the image at this defect thus have not only corrected amplitudes that are higher than the points that surround them, but their amplitudes are intercorrelated with each other, i.e. they have a coherence over several spatially adjacent positions at the defect.
  • the image has a much lower inter-correlation around any point whatsoever.
  • each gash can be detected by a spatial persistence on the image according to the abscissa and/or the depth where it appears.
  • This spatial coherence is therefore used to highlight the useful signal representative of the defects to the detriment of the noise, less spatially correlated.
  • a spatial filtering using this spatial correlation can therefore be implemented on the corrected image, by applying a spatial filter to the corrected image so as to filter it spatially.
  • the spatial filter is designed to attenuate the variability of the structure noise, characterised by the spatial standard deviation of the distribution of its amplitudes, while still retaining the level of the signature of a defect which is revealed in the corrected amplitude of the corrected image.
  • the filter is said to be spatial since it does not involve any time considerations, the corrected image having corrected amplitudes that vary spatially, without time variation.
  • the spatial filter can be a one-dimensional filter applied on the component of abscissa a, i.e. for each depth p the corrected amplitudes I c (a) are filtered, and/or on the depth component p, i.e. for each abscissa a the corrected amplitudes I c (p) are filtered.
  • the spatial filter can be a low-pass filter.
  • the spatial cut-off frequency of the spatial low-pass filter can be chosen according to the minimum size ⁇ L min of the defects that are sought to be detected, as being the inverse of this minimum size ⁇ L min .
  • the spatial cut-off frequency is therefore chosen as being less than 100 m ⁇ 1 .
  • the spatial filter is typically a Butterworth filter.
  • the spatial filter can also be a two-dimensional spatial low-pass filter applied on the corrected image.
  • the frequency response in two dimensions can be chosen according to the minimum size of the defects sought, likewise for a uni-dimensional spatial filter.
  • the spatial filter can also be a median filter.
  • a bilateral filter as a spatial filter, which makes it possible to average the focused amplitude values of neighbouring pixels only if these values are close. This makes it possible to smooth the noise without decreasing the average amplitude of a possible defect, thus increasing the contrast of the image and highlighting the possible defect.
  • Implementing the proposed correction is then particularly advantageous since it makes it possible to homogenise the variability of the noise over the entire corrected image.
  • FIG. 3 c is an example of a filtered image resulting from a spatial filtering using a bilateral filter on the corrected image of FIG. 3 b . It is observed that the light zone 35 corresponding to the presence of the defect 13 is the only information present in the filtered corrected image, as all the noise has been eliminated by the spatial filtering.
  • the corrected image thus filtered makes it possible to obtain a detection map of the defects. Indeed, the signature appears on the corrected image, in particular via a different corrected amplitude of the surroundings, which makes it possible to detect them, but also to locate them.
  • a corrected image is a spatial representation, and each point is located via its depth and its abscissa.
  • a simple method of detection consists of using a given threshold: any exceeding of the threshold by a set of adjacent probed points w on the corrected image signals the presence of a defect.
  • Other more complex methods can of course be implemented.
  • a computer program product comprising program code instructions recorded on a non-transitory tangible medium that can be read by a computer for the execution of the method according to any preceding claim, when said program is executed on a computer.
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FR1857907 2018-09-03
FR1857907A FR3085481B1 (fr) 2018-09-03 2018-09-03 Procede de detection et de caracterisation par ultrasons de defauts dans un materiau heterogene
PCT/FR2019/052016 WO2020049247A1 (fr) 2018-09-03 2019-09-02 Procede de detection et de caracterisation par ultrasons de defauts dans un materiau heterogene

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